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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

OCA Successor of Singular Cardinal Uniformization Knaster 20M14 Singular Density diamond star PFA S-Space Shelah's Strong Hypothesis Souslin Tree Commutative cancellative semigroups Square-Brackets Partition Relations Forcing Martin's Axiom Aronszajn tree Universal Sequences Parameterized proxy principle Axiom R reflection principles Stevo Todorcevic Successor of Regular Cardinal Hedetniemi's conjecture Constructible Universe weak square Minimal Walks Distributive tree square principles tensor product graph square Forcing Axioms Whitehead Problem Weakly compact cardinal polarized partition relation stationary reflection Luzin set Generalized Clubs Large Cardinals Rock n' Roll Cardinal function Mandelbrot set Small forcing 05A17 very good scale Diamond Almost-disjoint famiy Prikry-type forcing Selective Ultrafilter Dushnik-Miller Rado's conjecture Ascent Path Cardinal Invariants Rainbow sets middle diamond Sakurai's Bell inequality Antichain free Boolean algebra Postprocessing function Cohen real Jonsson cardinal Prevalent singular cardinals Chromatic number HOD Foundations Almost Souslin Poset Absoluteness Chang's conjecture Partition Relations Erdos-Hajnal graphs approachability ideal Uniformly coherent Singular cardinals combinatorics Club Guessing Singular coﬁnality Hereditarily Lindelöf space weak diamond 11P99 super-Souslin tree Kurepa Hypothesis stationary hitting P-Ideal Dichotomy Hindman's Theorem Slim tree xbox Nonspecial tree projective Boolean algebra Non-saturation Erdos Cardinal PFA(S)[S] Almost countably chromatic b-scale Microscopic Approach Reduced Power Ostaszewski square L-space coloring number Fodor-type reflection Coherent tree sap ccc incompactness Fast club Fat stationary set

# Tag Archives: 03E50

## Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading